Geometric partitioning is fast and effective for load-balancing dynamic applications, particularly those requiring geometric locality of data (particle methods, crash simulations). We present, to our knowledge, the first parallel implementation of a multidimensional-jagged geometric partitioner. In contrast to the traditional recursive coordinate bisection algorithm (RCB), which recursively bisects subdomains perpendicular to their longest dimension until the desired number of parts is obtained, our algorithm does recursive multi-section with a given number of parts in each dimension. By computing multiple cut lines concurrently and intelligently deciding when to migrate data while computing the partition, we minimize data movement compared to efficient implementations of recursive bisection. We demonstrate the algorithm's scalability and quality relative to the RCB implementation in Zoltan on both real and synthetic datasets. Our experiments show that the proposed algorithm performs and scales better than RCB in terms of run-time without degrading the load balance. Our implementation partitions 24 billion points into 65,536 parts within a few seconds and exhibits near perfect weak scaling up to 6K cores.
For the purposes of making reliable first-principles predictions of defect energies in semiconductors, it is crucial to distinguish between effective-mass-like defects, which cannot be treated accurately with existing supercell methods, and deep defects, for which density functional theory calculations can yield reliable predictions of defect energy levels. The gallium antisite defect GaAs is often associated with the 78/203 meV shallow double acceptor in Ga-rich gallium arsenide. Within a conceptual framework of level patterns, analyses of structure and spin stabilization can be used within a supercell approach to distinguish localized deep defect states from shallow acceptors such as BAs. This systematic approach determines that the gallium antisite supercell results has signatures inconsistent with an effective mass state and cannot be the 78/203 shallow double acceptor. The properties of the Ga antisite in GaAs are described, total energy calculations that explicitly map onto asymptotic discrete localized bulk states predict that the Ga antisite is a deep double acceptor and has at least one deep donor state.
We describe new capabilities for modeling bilevel programs within the Pyomo modeling software. These capabilities include new modeling components that represent subproblems, modeling transformations for re-expressing models with bilevel structure in other forms, and optimize bilevel programs with meta-solvers that apply transformations and then perform op- timization on the resulting model. We illustrate the breadth of Pyomo's modeling capabilities for bilevel programs, and we describe how Pyomo's meta-solvers can perform local and global optimization of bilevel programs.
First-principles calculations are used to characterize the bulk elastic properties of cubic and tetragonal phase metal dihydrides, MH2 {M = Sc, Y, Ti, Zr, Hf, lanthanides} to gain insight into the mechanical properties that govern the aging behavior of rare-earth di-tritides as the constituent 3H, tritium, decays into 3He. As tritium decays, helium is inserted in the lattice, the helium migrates and collects into bubbles, that then can ultimately create sufficient internal pressure to rupture the material. The elastic properties of the materials are needed to construct effective mesoscale models of the process of bubble growth and fracture. Dihydrides of the scandium column and most of the rareearths crystalize into a cubic phase, while dihydrides from the next column, Ti, Zr, and Hf, distort instead into the tetragonal phase, indicating incipient instabilities in the phase and potentially significant changes in elastic properties. We report the computed elastic properties of these dihydrides, and also investigate the off-stoichiometric phases as He or vacancies accumulate. As helium builds up in the cubic phase, the shear moduli greatly soften, converting to the tetragonal phase. Conversely, the tetragonal phases convert very quickly to cubic with the removal of H from the lattice, while the cubic phases show little change with removal of H. The source and magnitude of the numerical and physical uncertainties in the modeling are analyzed and quantified to establish the level of confidence that can be placed in the computational results, and this quantified confidence is used to justify using the results to augment and even supplant experimental measurements.
Relaxed synchronization offers the potential for maintaining application scalability, by allowing many processes to make independent progress when some processes suffer delays. Yet the benefits of this approach for important parallel workloads have not been investigated in detail. In this paper, we use a validated simulation approach to explore the noise-mitigation effects of idealized nonblocking collectives, in workloads where these collectives are a major contributor to total execution time. Although nonblocking collectives are unlikely to provide significant noise mitigation to applications in the low operating system noise environments expected in next-generation high-performance computing systems, we show that they can potentially improve application runtime with respect to other noise types.
We introduce a meshfree discretization for a nonlocal diffusion problem using a localized basis of radial basis functions. Our method consists of a conforming radial basis of local Lagrange functions for a variational formulation of a volume constrained nonlocal diffusion equation. We also establish an L2 error estimate on the local Lagrange interpolant. The stiffness matrix is assembled by a special quadrature routine unique to the localized basis. Combining the quadrature method with the localized basis produces a well-conditioned, sparse, symmetric positive definite stiffness matrix. We demonstrate that both the continuum and discrete problems are well-posed and present numerical results for the convergence behavior of the radial basis function method. We explore approximating the solution to inhomogeneous differential equations by solving inhomogeneous nonlocal integral equations using the proposed radial basis function method.
Intrusion/anomaly detection systems are among the first lines of cyber defense. Commonly, they either use signatures or machine learning (ML) to identify threats, but fail to account for sophisticated attackers trying to circumvent them. We propose to embed machine learning within a game theoretic framework that performs adversarial modeling, develops methods for optimizing operational response based on ML, and integrates the resulting optimization codebase into the existing ML infrastructure developed by the Hybrid LDRD. Our approach addresses three key shortcomings of ML in adversarial settings: 1) resulting classifiers are typically deterministic and, therefore, easy to reverse engineer; 2) ML approaches only address the prediction problem, but do not prescribe how one should operationalize predictions, nor account for operational costs and constraints; and 3) ML approaches do not model attackers’ response and can be circumvented by sophisticated adversaries. The principal novelty of our approach is to construct an optimization framework that blends ML, operational considerations, and a model predicting attackers reaction, with the goal of computing optimal moving target defense. One important challenge is to construct a realistic model of an adversary that is tractable, yet realistic. We aim to advance the science of attacker modeling by considering game-theoretic methods, and by engaging experimental subjects with red teaming experience in trying to actively circumvent an intrusion detection system, and learning a predictive model of such circumvention activities. In addition, we will generate metrics to test that a particular model of an adversary is consistent with available data.
Evaluating the health of a mechanism requires more than just a binary evaluation of whether an operation was completed. It requires analyzing more comprehensive, full-field data. Health monitoring is a process of nondestructively identifying characteristics that indicate the fitness of an engineered component. In order to monitor unit health in a production setting, an automated test system must be created to capture the motion of mechanism parts in a real-time and non-intrusive manner. One way to accomplish this is by using high-speed video (HSV) and Digital Image Correlation (DIC). In this approach, individual frames of the video are analyzed to track the motion of mechanism components. The derived performance metrics allow for state-of-health monitoring and improved fidelity of mechanism modeling. The results are in-situ state-of-health identification and performance prediction. This paper introduces basic concepts of this test method, and discusses two main themes: the use of laser marking to add fiducial patterns to mechanism components, and new software developed to track objects with complex shapes, even as they move behind obstructions. Finally, the implementation of these tests into an automated tester is discussed.
Quantitative measures are proposed for characterizing the complexity of material models used in computational mechanics. The algorithms for evaluating these metrics operate on the mathematical equations in the model rather than a code implementation and are different from software complexity measures. The metrics do not rely on a physical understanding of the model, using instead only a formal statement of the equations. A new algorithm detects the dependencies, whether explicit or implicit, between all the variables. The resulting pattern of dependencies is expressed in a set of pathways, each of which represents a chain of dependence between the variables. These pathways provide the raw data used in the metrics, which correlate with the expected ease of understanding, coding, and applying the model. Usage of the ComplexityMetrics code is described, with examples.